Question

Describe the key characteristics of the graphs of rational functions of the form f(x)=(ax+b)/(cx+d). Explain how you can determine these characteristi

Rational functions
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asked 2021-05-22
Describe the key characteristics of the graphs of rational functions of the form \(\displaystyle{f{{\left({x}\right)}}}=\frac{{{a}{x}+{b}}}{{{c}{x}+{d}}}\). Explain how you can determine these characteristics using the equations of the functions. In what ways are the graphs of all the functions in this family alike? In what ways are they different? Use examples in your comparison.

Answers (1)

2021-05-23
This kind of function will have vertical asymptote at \(x=-(d/c)\), horizontal asymptote at \(y=a/c\). Its points of untersects will be: \((0,b/d)\) with y-axis \((-(b/d),0)\) with x-axis
For example, let`s take following function for values a=2, b=4, c=1. d=3: \(y=(2x+4)/(x+3)\)
This function will have: vertical asymptote" \(x=-(d/c)=-(3/1)=-3\) horizontal asymptote: \(y=a/c=2/1=2\) y-intercept: \(y=b/d=4/3\) x-intercept: \(x=-(b/a)=-(4/2)=-2\)
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